Ind. Eng. Chem. Res. 1992,31, 2524-2532
2524
Danckwerta, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970. Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions; Macmillan: New York, 1984, Vol. 2. Feige, M.; Lorenz, M.; Stopperka, K. Reaktionsbedingungen und Teilchengroseevon alpha-Fe00H. J. Signalaufzeichnungsmter. 1980, 8, 357. Feitknecht, W. The Oxidation of Solid Iron Hydroxides in Aqueous Solutions. Z. Elektrochem. 1959, 63, 34. Feitknecht, W.; Schindler, P. Principles of the Determination of Solubility Cohtanta of Hydroxide Precipitates; Pure Appl. Chem. 1963, 6 (2), 134. Francombe, M. H.; Rooksby, H. P. Structure Transformations Effected by the Dehydration of Diaspore Goethite and Delta Ferric Oxide. Clay Miner. Bull. 1959, 4, 1. Ledakowicz, S.; Nettelhoff, H.; Deckwer, W. D. Gas-Liquid Mass Transfer Data in a Stirred Autoclave Reactor. Znd. Eng. Chem. Fundam. 1984,23,510. Levenspiel, 0. The Chemical Reactor Omnibook +; OSU Book Stores: Corvallis, OR, 1984, Chapter 41. Mee, C. D. The Physics of Magnetic Recording; North-Holland: Amstermdam, 1964. Mieawa, T. The Thermodynamic Consideration for Fe-H20 System at 25deg.C. Corros. Sci. 1973, 13, 659. Misawa, T.; Haahimoto, K.; Shimodaira, S. The Mechanism of Formation of Iron Oxide and Oxyhydroxides in Aqueous Solutions at Room Temperature. Corros. Sci. 1974,14, 131. Miyamoto, S. The Effect of Alkali on the Oxidation of Ferrous Hydroxide with Air. Bull. Chem. SOC.Jpn. 1927, 2, 40. Miyamoto, S. On the Oxidation of Ferrous Hydroxide in Sodium Hydroxide Solution by Means of Air. Bull. Chem. SOC.Jpn. 1928, 3, 137. Nakata, K.; Iahikawa, T.; Amamota, T.; Kawamura, T. Process for the Preparation of Acicular-Fe00H. U.K. Patent 2111471B Sept 25, 1983. OConnor, D. L. The Crystal Growth of a-FeOOH (Goethite) in Aqueous Solution at High pH. D.Sc. Dissertation, Washington University, St. Louis, MO, 1990.
Ohlinger, M.; Schoenafhger, E.; Schneider, W.;Stritzinger, H.; Vaeth, G. Manufacture of Gamma-Iron(II1) Oxide. US. Patent 4061725 Dec 6,1977a. Ohlinger, M.; Schoenafiier, E.; Vaeth, G.; Stritzinger, H.; Koester, E.; Steck, W.; Schneehage, H. Manufacture of Acicular GammaIron(II1) Oxide. U.S. Patent 4061726 Dec 6, 1977b. Oswald, H. R.; Asper, R.; Lieth, R. M. A. Bivalent Metal Hydroxides. In Preparation and Crystal Growth of Materials with Layered Structures; Reidel: Dordrect, Holland, 1977. Ozaki, M.; Matijevic, E. Preparation and Magnetic Properties of Monodispersed Spindle-type gamma-Fe203 Particles. J. Colloid Interface Sci. 1985, 107, 199. Ramachandran, P. A.; Sharma,M. M. Absorption with Fast Reaction in a Slurry Containing Sparingly Soluble Fine Particles. Chem. Eng. Sci. 1969, 24, 1681. Sada, E.; Kumazawa, H.; Aoyama, M. Reaction Kinetics and Controls of Size and Shape of Goethite Fine Particles in the Production Process by Air Oxidation of Alkaline Suspension of Ferrous Hydroxide. Chem. Eng. Commun. 1988, 71, 73. Speliotis, D. E. Magnetic Recording Materials. J.Appl. Phys. 1967, 38, 1207. Vaeth, G.; Ohlinger, M.; Stritzinger, H.; Schoenafiier, E.; Wettstein, E.; Guth, W. Manufacture of Gamma-Iron(III)Oxide. U.S. Patent 4061727 Dec 6, 1977. Varlamov, A. V. Effect of the Concentration of Ferrous Hydroxide on the Particle Size Distribution of Goethite Powders. Lakokras. Mater. Zkh Primen. 1984,5, 7 (in Russian). Walpole, R. E.; Myers, R. H. Probability and Statistics for Engineers and Scientists; Macmillian: New York, 1972. Weast, R. C. Handbook of Chemistry and Physics; CRC Press: Cleveland, OH, 1975. Wohlfarth, E. P. Ferromagnetic Materials: A Handbook of the Properties of Magnetically Ordered Substances; Elsevier, North-Holland Amsterdam, 1980, Vols. 1-3.
Received for review December 30, 1991 Revised manuscript received August 17, 1992 Accepted August 27, 1992
Metal-Proton Equilibrium Relations in a Chelating Iminodiacetic Resin Federico Mijangos* Department of Chemical Engineering, University of Pais Vasco, Bilbao, Spain
Mario Diaz Department of Chemical Engineering, University of Oviedo, Oviedo, Spain
A model of equilibrium including the pH effect was proposed and tested with experimental data of the Na-H-metal systems onto chelating resins. The protonation constanta were used to calculate the complexing capacity of the metals Cu, Ni, Co, and Zn in the iminodiacetic type resin. This equilibrium model that considers two stoichiometries for the retention of divalent nonferrous metals was extended for simultaneous multimetallic uptake and applied to a real hydrometallurgical effluent. Another simplified equilibrium model that only requires one equilibrium constant for each metal has shown to fit fairly well the experimental results.
Introduction The design of ion exchange equipment for effluent treatment requires, among other topics, a good knowledge of metal load from the complex solution usually involved. Nevertheless, it is unusual to find data reporta and model applications for this kind of systems. One of them is the publication of Marcus and Howery (1975)that reports equilibrium constants for many ion exchangers and systems. Marinsky (1986)and Shallcross et al. (1988)give a good overview on the thermodynamic bases,data feasibility, and equation manipulation. On the other hand, most of the literature concerning chelating resins uses the distribution coefficient to characterize the equilibrium for only one heavy metal. At present, chelating resins (also iminodi-
acetic acid type) have been widely investigated but almost always using simple synthetic solutions (Eger et al., 1968; Millar, 1989). Otherwise, the works are only a report of the experimental results. Unfortunately, chelating resins are mostly used in hydrometallurgy where the solutione involved usually contain several cations and very little work has been done in relation with metal retention from real complex media (Diaz and Mijangos, 1987;Hubicki, 1986;Kauzcor et al. 1973, 1974; Kennedy et al., 1987; Mijangos and Diaz, 1990; Mijangoe et aL, 1990,Seftan, 1978;Strong and Henry, 1976; Tare et al., 1984). Literature on heavy metal equilibria in this field was written in the 1960s or early 1970s (Leyden and Underwood, 1964; Loewenschuss and Schmuckler, 1964;
osss-~ss~/~2/2~3i-252~~~3.00/0 0 1992 American Chemical Society
Ind. Eng. Chem. Res., Vol. 31,No. 11,1992 2525 Schmuckler, 1965;Hering, 1967;Eger et al., 1968; Millar, 1989), and in recent years authors have dedicated their efforts to kinetics studies (Helfferich, 1983) or special applications (Streat, 1986). Although kinetics studies and theory of ion exchange have developed to such an extent that models for kinetics in multispecies systems and simultaneous chemical reactions are now available (Hwang and Helfferich, 1986;Yoshida et al., 1986),these sophisticated tools could be improved by an equilibrium model which is applicable for a wide range of conditions. For chelating resin, it is necessary that the equilibrium model considers explicitly the pH effect and the metalmetal interaction of the solution because normally an important change in pH occurs during the reaction inside the bead and a real solution contains several cations in different concentrations that modify the chelating behavior. Nevertheless, only a few works have been published dealing with this variable for metal load prediction, especially in complex media (Grinstead, 1984,Leyden and Underwood, 1964; Mijangos et al., 1987). As an initial step in the analysis of this problem, the stability protonation constants have to be determined. The iminodiaceticresin is quite complex, because its functional group is able to attach three protons or a multivalent metal in a certain spatial coordination. Various other factors that affect the load of the species have been indicated, Le., osmotic pressure effects, nonelectrolyte adsorption, and free-water content, among others. On the other hand, the active group concentration inside the resin can be as high as 5-10 mol/L free water, so activity coefficients cannot be accurately estimated, especially in the case of complex solution as Marinsky discusses (1983). However, Rossoti considers that, due to the large number of interactions, activity coefficients can be considered to be constant so the standard state could be even defined for the average internal concentration (Rossoti, 1978). This paper deals with the topic described above. Firstly, the complexing of different metals was analyzed when the substitution of Na-H occurs to a certain extent related with the external pH value. Previously, the protonation constants for the Na-H system were determined. Equilibrium data have been fitted to equations which assume simultaneous metal and proton retention from complex media. We expect these equations will be able to deal with metal equilibrium from multimetallic solutions. Then, an ion exchange equilibrium model for multimetallic uptake from a hydrometallurgical solution has been developed for this chelating resin. In our opinion this model may be useful in correlating experimental results by means of a short group of parameters in a wide range of pH and compositions. This model has been tested before against experimental results obtained with a monometallic synthetic hydrometallurgical effluent. After that, an attempt was made to predict experimental results in a multimetallic solution. Finally, a more simple model was also proposed to avoid the constants connected with the less quantitatively important chelate. That was because of the complexity in the application of the former comprehensive model that uses three parameters for each metal and their constant values and even the coordination behavior change due to the interactions metal-metalchelating group.
Theoretical Aspects Iminodiacetic type resins have a ligand, -N(CH2COOH)2,that behaves as weak acid. It can attach another proton on the nitrogen for low pH, but them resins are usually applied in the sodium salt form in order to improve the operating capacity.
Table I. Protonation Constants for Iminodiacetic Group Attached to Commercial Resins and in Solution log @hi) LIGANDEX-I DOWEX A-1 IDAA" 1 9.12 8.58 9.32 2 12.27 11.65 11.89 3 13.71 14.0 13.77 a
IDAA = iminodiacetic acid in solution.
As a rule, protonation constants have been determined using eq 1 from potentiometric data (Hering, 1967;Krasner
and Marinsky, 1963; Leyden and Underwood, 1964). ah
However, this expression is not accurate when the functiond group is able to attach several protons. Because of this, it must be used separately for each one of the protonation steps. In the case just mentioned, a more general equation should be used (Roesotti, 1978): N
where ffh = N - [(added base) + (H) - (OH)] ( L / S ) / Q (3) This equation requires a nonlineer regression method for constants determination. In theae equations, concentrationsare defined inside the resin and so a relationship between them and the experimental values obtained from the external solution is required. In this work, as a consequence of the high ionic strength, we have considered that activity coefficients are constant. However, a solute distribution equation in membranes such as the Donnan expression could be used for this purpose (Marinsky, 1983). Considering the equation and assumptions described above for an iminodiacetic reein which can attach three protons onto its functional group, constants determination is possible directly from experimental data. (4)
These constanta have been calculated by several authors (ID& Bjerrum et al., 1958;Perrin, 1983;Sillen and Martell, 1964,DOWEX A-1: Krasner and Marinaky, 1963; Leyden and Underwood, 1964;LIGANDEX-I: Szabadka, 19821,and some of the published vdugs are shown in Table I. In these kinds of resin, metal and proton compete for the functional group. It has been obeerved that the amount of retained metals ie lower for lower externel pH and the full protonated resin is unable to retain most of the metals aa cations. Birney evaluated the uptake of chloro complexes at high acid concentrations (Birney et al., 1968). This functional group works with two different stoichiometric relations for metal chelation: for low metal concentration the ratio ligand/metal is 21,but with a large amount of metal the ratio 88 1:l (Brajter, 1971;Eger et al., 1968; Hering, 1967;Schmuckler, 1965). Overall stability constants for the two potential complexes can be defined by the general equations: (RM) . .
O1 = o(M)
2526 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992
and
4,
I
Nr -
Ionic strength ( M I
n- nn3 0 2013 0360
I
2
3
where symbols in parenthesea indicate activities inside the resin phase. For our purposes, the equilibrium is probably better defined as a first step in which very a low concentration of metal reacts with a great amount of resin and a second step where an additional portion of metal saturates the resin; then: 2R
+ M&R2M + M &
2RM
(7)
As a rule, the equilibrium constant for metal retention can be defined
where a conditional constant 9
k = Kq,'-O f(activity coefficients) = qR°Cb
(9)
can be defined. k considers implicitly activity, osmotic, and free-water influences. Considering real concentrations, two conditional constants can be defined accordinglywith these last steps.
+
q = q1 q2, the total amount of retained metal (both stoichiometries 2 1 and 1:l). Taking into account that the corresponding load of metals can be calculated by eqs 10 and 11, then q = cqR2(kl + k 2 / d
(12)
and from the maas balance over the functional group (eq 13) and the corresponding equilibrium equations, qR can be calculated from eq 14, which only depends on the experimental data (C,pH, 8):
8 = qR + qRH + qRH2 + qRH3 + 2ql +q2 = qRfW
-1 qR =
+ 2q1+
+ f(W1
(14)
where f(H) = [I + &(ll) + &(HI2
I
2I
I
4"
'
6
I
8
'
1
I
'0
Solution pH
Figure 1. Titration curves for commercial resin under analysis for different ionic strength levels.
finally left in the acid or base form by controlling the external pH. The acid-base capacity was measured in +e diprotic form of the resin which is obtained by washing the full protonated functional group. Heavy metals analysis was made using atomic abeorption spectrometry at standard conditions. Both external solution and the eluate with acid were analyzed. For equilibrium experiments, at least 8 h was required, but the experiment was only considered concluded when the external pH was constant.
Results and Discussion in Monometallic Solutions Protonation Equilibrium of the Functional Group. In order to obtain titration curves, different experimental methods and conditions have been used. Firstly, experiments were carried out at low ionic strength (0.003 M as average) by adding acid or base over the diprotic form of the resin. As the time required to end the experiments was too long, another two experiments were carried out with higher ionic strength (0.2 and 0.36 M ) using an automatic titrator. Finally, a set of vessels were used in order to equilibrate an amount of min with the external solution (ionic strength 1.00 M) at different pH values, this method having been used and well-described by Szabadka (1982). The results are shown in Figure 1. The protonated fraction of the resin was calculated from experimental results using eq 3, and then the conditional stability constant was calculated using eq 2 for three protons, N = 3.
q2 (13)
+ [ l + *8klCQ/(k& + f(H))2]"2 4klC/[k&
-6l0
8h3(H)3]"
(15)
It is necessary to use the mass balance applied to the metal when the amount of metal retained is high. C&, = CL + q s (16) L = Lo+ qa,so L is the volume of the external solution plus the internal water content.
Experimental Section The experiments have been carried out in a batch setup at constant temperature and ionic strength. The solution pH was continuously measured, but it can be changed slightly to the desired final value by adding acid or base. The resin (Lewatit TP 207) was conditioned using treatment with several steps of acid wash-base wash and
Although this equation can be linearized,the calculated values of the constants did not correlate adequately with the experimental results. Therefore a nonlinear regreaion method was used. The optimum value of the conatants was log (Ow) = 9.72, 13.32, and 14.27, for j = 1, 2, and 3, respectively. These values are similar to those obtained by several authors using different techniques and conditions as has been previously shown in Table I. These results are useful not only for modeling metal retention onto this type of resin but also for selecting the best conditions in the regeneration step in which the protonated resin is transferred to the sodic form. Aa this step is very fast, it can be designed with equilibrium conditions, so consumption, concentration, and best ionic form can be calculated from the previous equation with the above given constant values. Metal Distribution in Ternary System. Experiments were carried out in the batch system deacribed above using a synthetic solution of one metallic cation (10.0 g/L), sodium chloride (1.0 g/L chloride), and sodium sulfate (3.0 g/L sulfate), but in experiments about the effect of the
Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 2527 Table 11. Experimental Results of Metal Uptake onto the Iminodiacetic Type Resin at High Metal Concentration PH C (mol/L) Q (mol/kg) PH C (mol/L) 4 (mol/kg) Cobalt 0.00 0.170 0.001 2.02 0.168 0.&49 0.91 0.170 0.070 2.99 0.166 1.919 1.50 0.170 0.165 3.W 0.165 2.650 2.01 0.169 0.676 4.03 0.165 2.345
Table IV. Logarithm of the Conditional Constants (kl and k2,L kg mol-2and L mol-l, Respectively) const copper nickel zinc cobalt kl 9.7 7.3 4.8 8.5 k2 6.70 5.61 5.23 4.90
Zinc 0.90 1.47 2.00 2.96
0.153 0.153 0.151 0.149
0.014 0.246 1.125 2.244
3.05 3.96 4.16
0.148 0.147 0.148
2.496 2.772 2.734
0.00 0.98 1.48 1.98
0.157 0.154 0.154 0.152
0.158 1.493 2.380 2.699
Copper 2.98 3.00 3.92 4.00
0.151 0.151 0.151 0.151
2.756 2.779 2.835 2.835
0.008 0.235 0.726 1.591
Nickel 2.13 2.96 3.00 4.06
0.00 0.98 1.55 1.90
0.170 0.170 0.169 0.167
0
0.166 0.165 0.164 0.164
1.879 2.704 2.765 2.834
Table 111. Equilibrium Metal Concentrations for Different Ion Chloride Concentrations DH (Cl-) (mol/L) C (mol/L) a (mol/kd Cobalt 1.570 3.31 0.03 0.014 0.014 1.570 3.24 1.00 3.27 3.00 0.014 1.706
1
2
3
L
5
Salutron pH
Figure 2. Experimental and calculated metal load at high concentration as a function of solution pH.
We used an objective function (eq 18) in order to optimize data (from Tables I1 and 111)correlations with the
~
Zinc 3.34 3.34 3.38
0.03 1.00 3.00
0.012 0.012 0.012
1.782 1.697 1.366
3.12 3.24 3.21
0.03 1.00 3.00
Copper 0.011 0.011 0.011
2.665 2.557 2.538
3.23 3.26 3.24
0.03 1.00 3.00
Nickel 0.013 0.013 0.013
2.079 2.053 2.028
chloride anion, sodium chloride was added in order to get different chloride concentrations. It has been considered that sodium cation does not affect chelation equilibria. Five hundred milliliters of this soluYon was used for each gram of dry resin in the sodium form. Because of this, the amount of retained metal is always less than 3% of the initial metal content in solution. The solution pH is controlled by adding a little amount of diluted hydrochloric acid. The amount of retained metal was measured by elution of the resin and the final solution concentration was calculated by mass balance. The experiments were carried out with solutions of copper, nickel, zinc, and cobalt. Experimental results are summarized in Table 11. The maximum retention observed for these metals was Q = 2.840 mol/kg dry resin in sodium form, and acid-base capacity is Qb = 5.680 mol/kg. It can be concluded therefore that in these conditions each mole of the functional group is able to retain 1 mol of those metals or 2 mol of sodium ion. However, from the literature, we know that for a very low metal concentration it is also possible that one metallic ion binds with two functional groups. Therefore we carried out another set of experiments with low metal concentration and with a different chloride concentration. These results are shown in Table 111. Higher chloride concentration gives rise to a considerable decrease of ainc retention.
previous equations (eqs 10-16). The parameters (k,and k 2 ) that optimize this function are shown in Table IV. The exponent of the protonation function (eq 15) gives the slope of the calculated c w e s qi VR pH. Therefore, the value which fits the experimental results was first determined, the result being n = '/, for every case teated. Then, this exponent was used in the definition of the function. In Figure 2, the experimental results for copper, nickel, zinc, and cobalt and those curves that were calculated using the above-mentionedequations and parameters are shown. In any case, the model fits the experimental results quite well but it can be observed that there is a better fitting for metals with higher values of kz. For copper and nickel data correlation is good, but zinc and cobalt show important differences. Moreover, the experimental results at low concentration are not low enough to calculate the first constant properly. This means that for more common wastewater problems the most important constant would be k,, but both should be used to fit properly the experimental data. Solving the previous equations (10-15), we can predict separately q1 and q2 and demonstrate that stoichiometry 2:l is important only for low concentrations and the selectivity could be modified by changing the external pH or metal concentration. We have compared these conditional constants with the values of the stability constants reported in the literature for the same ligand but in solution and concluded that there is a single relation between both values so other conditional constants (k,) can be evaluated from the data of stability constants available. In Figure 3, this relation is shown using EDTA data for copper, nickel, zinc, and cobalt. These results are very useful for predicting metal load as a function of the external pH. However, other effects such as metal speciation should be considered as in need of further study. These relations can be used to evaluate a range of conditions for which the separation of metals is adequate. The range of conditions is especially important during the elution in which an equilibrium between
2828 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 1
I
Lop KEora = 9 0 + 745 (Lo9 k2
sdutron Concrntrattm ( C / C o l
Figure 4. Predicted equilibrium diagram for a four metal solution-chelating resin system at conditions shown in Table V.
kli =
li -
f(B2, water content, activity coeff)
I
qR2ci
(19)
and q2i kzi = -- f(&, water content, activity coeff) qRCi The total amount of metal load is, in this case,
(20)
(21) qi = qli + q2i = kliqR2Ci + k2iqRCi Usually these equations will be applied in a system with a high level of salinity and a large number of species in solution (hydrometallurgicaleffluents),so it is almost impossible to calculate activity coefficients inside and also outside the resin due to the large number of interactions. Even the standard state can be defined for initial conditions, and therefore if the average concentrations are constant, we can assume that the interaction will be the same and the activity coefficients are constants (Roesoti, 1978). On the other hand, the maas balance over the functional group assumes that it can be found fully dissociated, protonated (three protons attachable), or chelating the metallic cations.
Q = qRf(H)+ 2Cq1i + Cqzi i
(22)
I
Combining with eq 19 and 20, the concentrationinside the resin of the (fully dissociated) functional group can be derived: -T + (P + 8Qxk1iCi)'/2
where f(H) hae being defined previously (eq 15). T = f(H) + CikziCi,but usually qR is a very low value, so the the
square-root term in eq 23 is approximately equal to P. Consequently it can be demonstrated that qR Q/T (24) Then, the amount of retained metal can be calculated directly by substituting eq 24 in the set of eqs 21 if there is no change in the external concentration, Ci. Otherwise mass balance over the metal (eq 16) is needed. Prediction of Metal Load from Monometallic Solution Data. Taking into account the valuea obtained for the conditional constants (&, kli, and k,) in the previous work, the initial concentrations (Cia), the functional group concentration inside the resin or capacity (Qb), the solid/liquid ratio, and the external pH, the equilibrium concentration (Ci and qi) can be calculated using an iterative method to solve the equations described above. Using a diagram of qi vs Ci, the domain of possible solutions to the set of equations is constrained by the limits of the initial concentration, an equilibrium isotherm, and the mass balance (eq 16). Then, the iteration starts by considering the initial solution concentrations as the equilibrium ones, so the concentrations of metals in the resin are calculated by the set of eqs 19-24. The intersection of the mass balance, eq 16, with the line that joins the calculated equilibrium point and the origin, is used as a way to evaluate new values of liquid concentrationsjust in its crossing point with the mass balance (eq 16). Then, a set of eqs 25 is obtained that gives solution concentra(25)
tions used for solving again the set of eqs 19-24 in the next iteration. In such a way, starting from the initial conditions (Cia), a first value for the solid concentrations is calculated (qJl and, for the second step, the solution concentration is calculated by eq 25 for each speciea. The process continues until no improvementa are obtained, on the basis of parameter s,, calculated by eq 26. Sn = [ ( C q i ) ,- (Cqi)n-112 (26) These methods have been introduced as a computer program which solves quickly each equilibrium point or obtains a whole set of isotherms for a constant solution pH. Predicted values of metal uptake are shown in Figure 4 for solution pH = 4.0, using parameters and conditions shown in Table V. In order to obtain different equilibrium points, an increasing liquid/solid ratio for each run has been taken. That is, basically, the program calculates four ( C , qi) equilibrium values for a set of initial conditions given: solution pH, solid/liquid ratio, and initial liquid concentrations. In this case, the equilibrium model has been applied for a two-phase system with four metallic
Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 2529 Table V. Starting Conditions and Parameters for Eauilibrium Prediction chelating resin iminodiacetic acid type (Lewatit TP 207) 2.64 resin metal load Capacity Q (mol/kg) cumulative protonation const (log &) 9.72,13.32,end 14.27 conditional stability conat kl (L kg-' mol-l), k2 (L mol-') 4.8 X log, 5.01 X l@ copper 2.2 X lo', 4.07 X lo6 nickel zinc 6.0 X lo', 1.70 X 106 3.4 x loe, 7.94 x lo' cobalt initial solution concn (mol/L) 2.05 X copper 1.70 x 10-3 nickel 30.60 x 10-3 zinc 2.05 X cobalt solution pH 4.0
components, although it can be applied for any number of metallic species. Figure 4 shows the predicted behavior of the system considering the equilibrium model prepared and the constant values calculated previously. Most of the total exchange capacity of the resin is used for copper and zinc uptake, but the curve of copper is always increasing and the corresponding curve for zinc shows a maximum of around C/Ci0 = 0.7. After that its concentration in the resin decreases when solution concentration increases. However, this 'paradoxical" behavior has really been observed in this and other different systems which involve competitiona between two or more species. An analogous conduct is observed for nickel and cobalt although these metals are retained in a lower range of concentration. So, as a consequence of this, an optimum value for the liquid/eolid ratio or liquid concentration is expected in order to separate those metals with less affiiity. It must be indicated that in Figure 4 an equilibrium state is determined by a line which crmes the isotherm from (1,O)and slope = -LC,/SQ. That is, it depends on the initial liquid concentration of each metal. These results agree qualitatively with those experimentally obtained. Results and Discussion for the Multimetallic System Diecureion on the Extended Model. Experiments have been carried out with the equipment and methods described previously, but in this case a real hydrometallurgical effluent has been used for the equilibrium experiments. This effluent is rejected by an industry dedicated to the recovery of metals from pyrite cinders. The compoeition of main components is as follows: chloride, 28.3;sulfate, 66.0;iron, 0.005;cobalt, 0.165;nickel, 0.100; copper, 0.130;&c, 2.00, manganem, 0.66; cadmium, 0.009; lead, 0.013; calcium, 0.41;KzO, 3.6;and NasO 45.0 g/L. This effluent has been previously treated in order to separata iron by a goethite process (Mijangm and Diaz, 1990; Mijangos et al., 1990). Metal recovery from this kind of solution c811 be carried out using chelating resin. Before, for this kind of solution, we selected the iminodiacetic acid type wing equilibrium a t a , among several kinds of reains (Mijangos and Diu, 1990; Mijangos et al., 1990). A quite important simplification in such a complex medium, which contains a large number of cations, is to consider only those cations retained in significant amounts. Thus,in this case only copper, nickel, zinc, and cobalt have been considered. The last, which has the lowest conditional constant, is always retained in amounts lower than 5 % of the whole capacity of the resin. Four sets of experiments have been carried out at constant external pH = 2.99, 3.87,4.25,and 4.62 (averaged)
0.8 l
'
O
02
0
04
V
06
1.0
0,8
1.2
C Imd/m3)
Figure 6. Experimental end fitted results of copper retention in the chelating resin for different solution pH levels. Solid line represents fitted values. 0.3
0
PH
I
0
I
I
I
I
I
10
05
I
15 C fmo//m3)
Figure 6. Experimental and fitted results of nickel retention in the chelating resin for different solution pH levels. Solid line represents predicted values.
3 20 30
10
C fmo//m')
Figure 7. Experimental end fitted results of zinc retention in the chelating resin for different solution pH levels. Solid line represents predicted values.
A 46
0
1.0
2.0 C /mol / m J l
Figure 8. Experimental and fitted results of cobalt retention in the chelating resin for different solution pH levels. Solid line represents predicted values.
and others at variable pH 3.3. Metal load VB solution concentration for each one of these cations is shown as experimental points in Figures 5-8. Predicted values of
2530 Ind. Eng. Chem. Res., Vol. 31, No. 11, 1992 Table VI. Logarithm of the Conditional Conrtonts Calculated by Nonlinear Regression induetrial synthetic solution solution cation CU(I1) Ni(I1) Zn(I1) Co(I1)
kl,
kB
kl,
10.05 4.51 8.70 7.76
4.59 4.25 1.02 3.42
9.7 7.3 4.8 8.5
kzr 6.70 5.61 5.23 4.90
metal load calculated using the equilibrium constants determined in synthetic solutions, shown in Table IV, do not predict properly the effect of pH on experimental metal load. Then, experimental results have been analyzed, fitting them to the proposed equations using the subroutine Complex (Box, 1965)for parameter estimation of nodhear equations. In Table VI the vdues calculated for the conswnts together with those for the synthetic monoherdic solution are shown. Although experimental reaulta were fitted to those predicted by the equations which were adequate for synthetic monometallic solutions containing the stme metals, there was a difference in curvature between the experimental and calculated curvw. ! This could be due to the difference in salinity in both media Monometallic solution contains a low level (0.1M) of chloride and sulfate while this industrial solution contains around 1 M of each salt, but the interaction metalmetal-functional group in this multimetallic system should be the main cause changing the coordination chemistry. A Simple Semiempirical Model. In order to improve manageability and fitting, the model can be simplified to avoid the constants in relation to the less quantitatively important complex. Moreover, constant values probably are modified in relation to the calculated values for synthetic monometallic solutions due to the interaction metal-metal-chelating group. Therefore, we have considered a new set of equations (eq 27) to correlate metal
retention with only one undefined parameter, ki, which should be evaluated from experimental results. For experiments carried out at constant external pH the apparent constant (eq 28),for each cation i, can be useful:
Therefore, arranging these equations, we can write
The values of a, b, and m can be calculated by adjusting the experimental results for each metal to eq 29. We found out that values of 2,2,and 1 for a, b, and m,respectively, give the best fitting. In Figures 5-8 the experimental results and the calculated values for those experiments carried out at constant pH are shown. It should be pointed out that one equilibrium point is represented simultaneously in Figures 7 and 8 (equilibrium state is defined by the concentrations of copper, nickel, zinc, and cobalt) because equilibrium cannot be solved for each metal separately. The apparent constants calculated for different experimental conditions are shown in Table VII. Taking into account distribution coefficients (qi/Ci)and in accordance with the prediction from the synthetic solution, we can observe that the order of selectivity (ratio of distribution coefficients) is copper, nickel, zinc (that is
Table VII. Apparent Constants (L mol-') Calculated from Experiments with Industrial Solution for Different pH Values and Cobalt Concentrations (mol/L) exDerimental conditions aDDarent constants pH logf(H) (Co) copper nickel zinc- cobalt 2.99 3.72 1.83 X 190 2.26 3.30 0.55 3.87 3.02 1.83 X 500 14.1 24.4 2.8 2960 41.8 51.6 4.25 2.78 1.83 X 4.5 4.62 2.51 1.83 X 740 25.0 55.0 4.8 3.65 3.17 5.09 X 750 17.1 19.6 3.0 3.65 3.17 10.86 X 620 11.0 22.9 4.2 3.17 15.27 X 730 12.6 22.6 3.65 5.7 1
51
t. 0
21 2 5
I
cu NI
30
35 log
LO
m
Figure 9. Representation of the logarithmic valuea of k i / k / v8 f ( H ) .
retained in higher amounts), and finally cobalt. We can also observe in these figures that the lower the selectivity is, the higher the dispersion of experimental data is, so the isotherms for copper are well-defined but cobalt isotherms are not so well-defined. The effect of pH and cobalt concentration on the equilibrium parameters is shown in Table VII. Cobalt concentration ranging between 5.04 X and 15.27 X mol/L does not affect other apparent constant values, except for cobalt itself for which a slight variation seems to be observed. A quadratic dependence on the solution concentration of cobalt could fit these results better, but for the sake of applicability it could be useful to consider the same basic equation for the same kind of cation (nonferrous metals in this case). On the other hand, the calculated constants increase with external solution pH but a maximum is observed for copper and nickel load at pH 4.25. This effect is probably due to the formation of basic species. The conditional constanta kiwhich will be independent of pH were calculated using eq 28. This was done from a log k[ VB log f(H) plot where n values 0.5,1.0,and 2.0 were tested, the best being 1.0,and then values of ki were calculated for each metal from the ordinate at the origin. In Figure 9 the goodness of the fitting to eq 28 with n = 1 is shown for nickel, zinc, cobalt, and copper. The dependence of metal retention over the external pH is the same for this industrial solution and with the synthetic monometallic solution. The valuea of the conditional constants, ki, are 1.05 X lo6, 1.58 X lo4,2.24 X lo4,and 2.82 X lo3 L mol-' for copper, nickel, zinc, and cobalt, respectively. These constants are independent of the external solution pH, but the effect of this variable over the metal load can be predicted by means of the function f ( H ) previously defined. These equations and constants are only adequate for external solution pH lower than 4.2 because for more alkaline media several basic species are possible and even precipitates of copper are posaible. Speciation or solubility equilibria should be considered in order to develop a more exhaustive treatment. Nevertheless, the model could be easily extended by calculating the effective metal con-
-
Ind. Eng. Chem. Res., Vol. 31, No. 11,1992 2531 centration in solution from the solubility products.
Conclusions In this work, we have proposed basic equilibrium equations for simultaneous protonation and metal load reactions for a commercial ion exchange resin (iminodiacetic group). These relations are able to correlate the experimental results and to predict the resin behavior with metal eolutions of high salinity. The calculatedconditional constants & and ki are in good agreement with those values taken from the literature. The effect of external solution pH can be taken into account through these basic equilibrium equations that disregard (i) concentration differences between inside and outeide phases, (ii) activity coefficients values, and (iii) specific interactionsmetal-metal-proton-chelating except the main competition chelating reaction. Theee equations are able to predict metal retention from monometallic solution but only qualitatively metal load from complex solution. It appears that the interaction between ions modified the equilibrium behavior. Then, we have proposed another simplified equilibrium model which allows manageability and fitting of experimental results. This model involvea only a constant for each nonferrous cation and can predict metal load in a wide range of conditions for this specific system. Moreover, the model can be easily applied to other chelating resins and solutions. Nomenclature a = stoichiometric coefficient b = stoichiometric coefficient C = metal concentration in the liquid phase (mol/L) f(H) = function of the proton concentration, eq 15 K 5 stability conetants k = conditional constante k' = apparent constants L = volume of solution considering the resin internal content
(L)
M = metal m = stoichiometric coefficient n = exponent of the proton function (eq 15) N = number of protons of a polyprotic functional group Q = ion exchange capacity (mol/kg dry resin) q = resin uptake (mol/kg dry resin) R = base form of the functional group RHj = partially protonated functional group R,Mb = functional groupmetal chelate (stoichiometry a:b) S = mass of dry sodium-form resin (kg) S, = fitting index, eq 26 Subscripts cal = calculated exp 5 experimental b = acid-base h * protonation i = metallic cations j = protonation step of a acid with N protons n = number of iteration w = water 0 = initial values or conditions 1,2 = chelating stoichiometries, 2:l and 1:1,respectively Greek Symbols a h = degree of protonation B = overall stability constante Registry No. Co, 7440-484 Cu, 7440-50-8; Zn,7440-66-6; Ni, 7440-02-0.
Literature Cited Birney, I>. G.; Blake, W. E.; Meldrum, P. R.;Peach, M. E. Adsorption of chloro-complexes of the first row transition elementa by
Dowex A-1. Talanta 1968,15 (6), 557-559. Bjerrun, G.; Schwarzenbach, G.; Sillen, L. G. Stability Constant of Metal-ion Complexes with Solubility Products of Inorganic Compounds; The Chemical Society: London, 1968. Box, M. J. A New Method of Constrained Optimization and a Comparation with Other Methods. Comput. J. 1965,1, 42-52. Brajter, K. E.amination of Complexhg Properties of CHELEX 100 Ion Exchange Resin. Chem. Anal. 1971,16,587-593. Dim, M.; Mijangos, F. Metal Recovery from Hydrometallurgical Wastes. J. Met. 1987, 39 (7), 42-44. Eger, L.; Anapach; Marinsky, J. A. The Coordination Behaviour of Cobalt, Nickel, Copper and Zinc in a Chelating Ion Exchange Resin. I & 11. J. Znorg. Nucl. Chem. 1968, 30, 1899-1924. Grinstead, R. R. Selective Adsorption of Copper, Nickel, Cobalt and other Transition Metal Ions from sulfuric Acid Solutionswith the Chelating Ion Exchange b i n XFS 4195. Hydrometallurgy 1984, 12,387-400.
Helfferich, F. Ion Exchange Kinetics-Evolution of a Theory. In Mass Transfer and Kinetics of Zon Exchange; NATO AS1 Series,Series E 71; Nijhoff: The Hague, 1983; pp 157-179. Hering, R. Chelatbildende Zonenawtawcher; Akademie Verlag: Berlin, 1967. Hubicki, 2.Purification of Nickel Sulfate Using Chelating Ion Exchangers and Weak-Base Anion Exchangers. Hydrometallurgy 1968,16, 361-375.
Hwang, Y.; Helfferich, F. Generalized Model for Multispecies Ionexchange Kinetics including Fast Reversible Reactions. React. Polym. 1986,5,237-253. Kauczor, H. W. Recovery of Nickel by Ion Exchange, Znst. Chem. Eng. Symp. Ser. 1975,42, 25-28. Kauczor, H. W.; Hunghanss, H.; Roever, W. The Hydrometallurgy of Metalliferoue Solutions in the Processing of Manganese Nodules. Luter-Ocean'73,Kongreaa-Berichtawerk, Vol. I; Technieche Universiat Berlin: Berlin, 1973; Lewatit. 1973. Bayer AG Technical Paper; Order No. OC/I 20336e, 1974. Kennedy, D. C.; Becker, A. P.; Worcester, A. A. Development of an Ion Exchange Process to Recover Cobalt and Nickel from Primary Lead Smelter Reaidues. Metals Speciation, Separation and Recovery; Lewis: Chelsea, 1987; pp 593-613. Krasner, J.; Marinsky, J. A. The Dissociation of the Iminodiacetic Acid Groups Incorporated in a Chelating Ion Exchange Resin. J. Phys. Chem. 1963,67, 2559. Leyden, D. E.; Underwood, A. L. Equilibrium Studies with the Chelating Ion &change k i n Dowex A-I. J. Phys. Chem. 1964, 68,2093.
Loewenechuss, H.; Schmuckler, G. Chelating Properties of the Chelating Ion Exchanger Dowex A-1. Talanta 1964,11,1399-1408. Marcus, M.; Howery, D. G. Zon Exchange Equilibrium Constants; IUPAC Additional Publication, Butterworth London, 1975. Marinsky, J. A. Selectivity and Ion Speciation in Cation-Exchange Resins. In Mass Transfer and Kinetics of Zon Exchange; NATO AS1 Series, Series E 71; Nijhoff: The Hague, 1983; pp 75-120. Mijangos, F.; Dw,M. Ion Exchange Recovery of Metals from Waste Water of Complex Sulfide Hydrometallurgy. Hydrometallurgy 1990,23, 365-375.
Mijangos, F.; Irabien, A.; D i u , M. Equilibria y simulacih de retenci6n de cobalto por resina de intercambio ibnico de amidoxima en tanque agitado. An. Quim. 1987,83,358-363. Mijangos, F.; Lombraiia,J. I.; Varona, F.; Diaz, M. Extraction of non Ferrous Metals from Hydrometallurgical Waste Waters. Znst. Chem. Eng., Symp. Ser. 1990,119,61-78. Millar, J. R. 'Design, Synthesis and Applications of Chelating Ion Exchange Resins"; IRSA Internal Report, CNR Italy, 1989. Perrin, D. D., Ed. Stability Constants for Metal-Zon Complexes. Part B Organic Ligand. IUPAC Chemical Data No. 22; 2nd ed.; 1983.
Roesotti, H. The Study of Ionic Equilibria. An Introduction; Longman: London, 1978; pp 11,36,55. Schmuckler, G. Chelating Resins. Their Analytical Properties and Applications. Talanta 1966,12,281-290. Sefton, C. Selective Recovery of Nickel and Cobalt or Copper and Zinc from Solution. U.S. Patent 4,123,260, October 1978. ShaIlcm, D. C.; Herrmann, C. C.; McCoy, B. J. An Improved Model for the Prediction of Multicomponent Ion Exchange Equilibria. Chem. Eng. Sci. 1988,43 (2), 279-288. Sillen, L. G.; Martell, A. E. Stability Constants of Metal-ion Complexes; Chemical Society: London, 1964. Streat, M. Application of Ion &change in Hydrometallurgy. In Zon Exchange: Science and Technology; NATO AS1 Series, Series E, 107; Nijhoff: Dordrecht, 1986; pp 449-461.
Znd. Eng. Chem. Res. 1992,31, 2532-2538
2632
Strong, B.; Henry, R.P. The Purification of Cobalt Advance Electrolyte wing Ion Exchange. Hydrometallurgy 1976, I, 311-317. Szabadka, 0.Studies on Chelating b i n s . 11. Determination of the Protonation Constanta of a Chelating Resin Containing Iminodiacetic Acid Groups. Talanta 1982,29, 183-181. Tare, V.;Karra, S. B.; Haas, C. N. Kinetics of Metal Removal by Chelating Resin from a Complex Synthetic Waate Water. Water,
Air Soil Pollut. 1984, 24 (4), 429-439. Yoshida, H.; Kataoka, T.; Fujikawa, S. Kinetics in a Chelating Ion Exchanger. Chem. Eng. Sci. 1986,41 (lo),2511-2530. Received for reuiew September 26,1991 Revised manuscript receiued February 19, 1992 Accepted July 11,1992
PROCESS ENGINEERING AND DESIGN Evaluation of Operating Procedures Based on Stationary-State Stability Vital Adion,+Jayant Kalagnanam,t and Gary J. Powers*?+ Department of Chemical Engineering and Department of Engineering and Public Policy, Carnegie Mellon Uniuersity, Pittsburgh, Pennsylvania 15213
The safe and reliable operation of chemical planta depends on high-integrity operating procedures. Such procedures often involve process transition through stationary states. The stability of these states is an important part of the integrity evaluation. The methodology presented in this paper qualitatively identifies families of inherently stable chemical operations and establishes design rules for the synthesis of stable stationary states. These rules have been developed using the RouthHuiwitz conditions for three qualitative levels of dynamic system models. These levels represent the gains of the dynamic system by the signs of the gains (+, 0, -), the signs and their equality (+, 0,-, =), and finally the gains represented by their order of magnitude values (+, 0, -, =, ). Example design rules have been developed during the synthesis of operating procedures for a series of vessels with composition control and temperature control of an exothermic chemical reaction. The most robust design rules apply to systems that can be proven stable by the sign level of gain representation. Less robust rules with a wider range of applicability to dynamic systems have been developed using the equality and order of magnitude representations. 1. Introduction Operating procedures are instrumental in the safe, reliable, and environmentally sound operation of a chemical plant. The synthesis of high-integrityoperating procedures commonly incorporates deairable features, such as verifiability of procedure steps and stability of intermediate procees states. Operating procedures takes a process from an initial to a goal state. This state transformation is achieved by applying permissible process operations, without violating process constraints. These constraints are motivated by concerns for the safe and reliable operation of the plant. Environmental impact, quality control, and economic issues also influence the synthesis of operating procedures. The concerns for safety and reliability favor processes which are inherently stable over large ranges of parameter values and operating conditions. Such processes face a lower risk of undesirable scenarios, like explosions, runaway reactions, and unacceptably high vessel pressure. Assessing stability early in the design aims to produce processes with inherently favorable operating characteristics. The methodology presented in this paper qualitatively identifies families of inherently stable chemical operations. Qualitative analysis is used to evaluate stability at three levels of process information. The results of the
* Author to whom correspondence should be addressed. t Department
of Chemical Engineering.
* Department of Engineering and Public Policy.
proposed evaluation may be used as general design rules for the synthesis of stable atationary states in high-integrity operating procedures. 1.1. Recent Work in Operating Procedure Synthesis. The methodologies for operating procedure synthesis have included a variety of symbolic manipulation techniques to generate desirable plans. h i l l 0 and Powers (1987, 1988a,b) uaed a modified form of means/ends analysis, where operating goals were identified and procedural actions were sought to satisfy the goals. A constraint-guided strategy searched for sequences of actions that did not violate the operating constraints. The methodology decompoeed the complexity of the system by exploiting the existence of stationary states,or states where the operating goals are partially met and the system can wait. These states were used as planning islands, where the status of the system can be verified before the next planning action is taken. Lakshmanan and Stephanopoulos (1988a,b, 1990) developed hierarchical, object-oriented modeling techniques and applied them with a nonlinear planning method to synthesize operating procedures for chemical plants. Models were implemented as objects, allowing relations and methods to be inherited through the hierarchy of models. Their planning methodology involved identifying stationary states and using means/ends analysis to plan procedures for carrying the process between stationary states. The nonlinear planning techniques were based on the propagation of constraints. They also aeveloped specific methodologies addressing qualitative mixing con-
0888-5885/92/2631-2532$03.00/00 1992 American Chemical Society
